Maybe some dips and something to work your lower back, like back extensions?
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Dave LiepmannFeb 12 '13 at 1:23

@user1935358 I need to refine my answer a bit but I'm really swamped with work right now. I'll talk a little bit more about torque and torsion forces of the deadlift -- it really can't be simulated with other movements, but maybe you're ok with omitting it. Stay tuned.
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DanielFeb 12 '13 at 14:41

Squat enhanced with backpack do not cover for deadlifts.
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KateFeb 12 '13 at 16:40

3 Answers
3

You're lacking exercises that involve significant engagement of the shoulder and posterior chain. A good rule of thumb is to include all of the "big five" exercises (or some variation of them) as a foundation. The big five are:

You're doing pull-ups -- and they are an excellent exercise that you should definitely keep in your routine -- but by only including a downward rotation movement, you're missing out on engagement of the upper back (see the adduction articulation) and core involvement to properly balance-out the push-up (analysis on that here).

If you aren't able to use free weights for these, you can include inverted rows. Use a loaded backpack for more resistance.

It's a shame you can't do these with weight. As Renny suggested, doing pistol squats (single leg squats) would be an excellent alternative. I also recommend sissy squats. You can always increase the resistance of these with a weight vest.

These are the most practical and fundamental of all exercises. Picking something up off of the ground is an essential human movement. This question is pretty spot-on. Berin is right in saying that there really just is no real alternative.

I can't find the exact resource I was looking for (I believe it was a talk by Kelly Starrett) about analysis on the shear, torsion, and torque forces applied to the spine and hips, but I was able to find this mechanical analysis that covers them in some detail. Essentially, the alternatives to the deadlift can't produce anywhere near the same amounts of forces on the spine as the deadlift. What this means is that the entire waist (spinal erectors, abdominal erectors, etc) and many of the hip rotators and flexors only receive their maximum possible engagement with a floor pull.

Aside from that, there are many other benefits to doing deadlifts, such as maximal isometric engagement of the gripping muscles, enormous forces applied to the upper back (presently you are lacking any real trapezius engagement -- perhaps include some inverted shrugs), maximal glute engagement, and so on. It's really a shame to omit this exercise, but if you must, see Berin's post or maybe check out this resource.

Edit:

OP asks if his or her routine is complete.

Barring deadlifts and including a bodyweight shoulder press, I think you've got a pretty good collection of movements put together. There are a lot of calisthenic-only bodybuilders out there that have had a great deal of success. Unfortunately without including some kind of pull from the floor, there's no way you could get a trunk like this. But, the more you can overload your bodyweight movements, the better your results will become over time. Just keep making it more difficult and keep at it -- that routine will work out great!

I also do not see any exercises that really work the lower back, bulking up on muscle while neglecting lower back can lead to poor posture and back pain. I would recommend deadlifts or hyperextensions.

I agree with Doc, you could be working your vertical shoulder movements more. If you absolutely cannot include weight exercises in your training, you could try more advanced shoulder exercises like incline push-ups (starting with your feet on an elevated surface, like a bed, gradually increasing the incline all the way up to a handstand push-up against a wall (video: http://www.youtube.com/watch?v=JGhdSLkf-8o).

I also recommend single leg squats when you begin to feel like the squats are too easy (which in my experience, happens quite quickly), however the learning curve is sharp. I recommend you check out http://www.beastskills.com, the guy that posts here has very good instructions on form and how to ease your way into more advanced exercises.